Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you find the derivative of #f(x)=-5x# using the limit process?

1 Answer

Nov 3, 2017

see below

Explanation:

the definition

#(dy)/(dx)=Lim_(hrarr0)((f(x+h)-f(x))/h)#

#f(x)=-5x#

#(dy)/(dx)=Lim_(hrarr0)((-5(x+h)- (-5x))/h)#

#(dy)/(dx)=Lim_(hrarr0)((cancel(-5x)-5hcancel(+5x))/h)#

#(dy)/(dx)=Lim_(hrarr0)((-5cancel(h))/cancel(h))#

#(dy)/(dx)=Lim_(hrarr0)(-5)=-5#

Related questions

What is the limit definition of the derivative of the function #y=f(x)# ?
Ho do I use the limit definition of derivative to find #f'(x)# for #f(x)=3x^2+x# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(x+3)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/(1-x)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=x^3-2# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/sqrt(x)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=5x-9x^2# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(2+6x)# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=mx+b# ?
How do I use the limit definition of derivative to find #f'(x)# for #f(x)=c# ?

See all questions in Limit Definition of Derivative

Impact of this question

3588 views around the world

You can reuse this answer
Creative Commons License